What is equilateral triangle ?

In geometry, an equilateral triangle is a triangle in which all three sides are equal. The area enclosed by this shape is known as area of equilateral triangle.

Area of equilateral triangle can be found using the formula given below.

**Area of Equilateral Triangle = (√3/4)a ^{2 }sq. units**

where a is the length of each side of the triangle.

Take an equilateral triangle of the side “a” units. Then draw a perpendicular bisector to the base of height “h”.

By drawing perpendicular from A, we get two congurent right triangle ABD and ADC.

Area of triangle ABC = Area of triangle ABD + Area of triangle ADC

Since triangles ABD and ADC are congurent, areas will be equal.

Area of triangle ABC = Area of ABD + Area of ADC

Area of triangle ABC = 2 (Area of ABD)

= 2 ⋅ (1/2) ⋅ Base ⋅ Height

Area of triangle ABC = Base ⋅ Height ---(1)

In triangle ABD,

Base (BD) = a/2 and height (AD) = h

Using Pythagorean theorem,

a^{2} = h^{2} + (a/2)^{2}

h^{2 }= a^{2 }- (a^{2}/4)

h^{2 }= (3a^{2}/4)

h = √(3a^{2}/4)

h = (a√3/2)

By applying the values of base and height in (1), we get

Area of triangle ABC = (a/2) ⋅ (a√3/2)

= (1/4)a^{2}√3

Area of triangle ABC = √3a^{2}/4 square units

**Example 1 :**

Find the area of the equilateral triangle having the length of the side equals 10 cm.

**Solution :**

Area of equilateral triangle = (√3/4) a²

Here a = 10 cm

= (√3/4) (10)²

= (√3/4) x (10) x (10)

= (√3) x (5) x (5)

= 25 √3 cm²

**Example 2 :**

Find the length of the altitude of an equilateral triangle of side 3√3 cm.

**Solution :**

Side length of equilateral triangle (a) = 3√3

Area of equilateral triangle = (√3/4) a²

= (√3/4) (3√3)²

= (√3/4) (27)

Area of equilateral triangle = 27√3 / 4 ---(1)

Here we should find the length of altitude, so we use the formula base ⋅ height to find the area of equilateral triangle.

= base ⋅ height

= (3√3/2) ⋅ h ------(2)

(1) = (2)

(3√3/2) ⋅ h = 27√3/4

h = (27√3/4) ⋅ (2/3√3)

h = 9/2

h = 4.5

So, the required height is 4.5 cm.

After having gone through the stuff given above, we hope that the students would have understood how we derive the formula for area of equilateral triangle and examples.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**